Vertex Group Weights disappear when I move the bone
Every modifier has three or four display options.



The first one shows the result of the modifier when rendering.

The second shows the result in the viewport.

The third shows the result while in edit mode

The fourth shows the result on the edit cage while in edit mode. Enabling this only works when the third is enabled.

By having the edit mesh options disabled, you will only see the undeformed mesh in edit mode. Enable both of these to have the edit mesh follow the armature.

While in edit mode, selecting bones has no effect on the display of vertex group weights. Select a vertex group in the mesh properties to change the weights displayed in the viewport.